In a large mixing bowl, whisk egg, sugar, buttermilk, coconut milk, melted butter and vanilla extract together until smooth.
Sift in all dry ingredients and whisk until all incorporated.
Transfer batter into a piping bag. (You may have to do it in two takes or the bag will be too full to pipe.)
Cut the tip off both piping bag, leaving only about ½ inch opening.
Squeeze batter into the donut cups of the pan, filling them. Make sure there is an even amount of batter all around.
Bake for 10-11 minutes and cool on the wire rack until they can be handled. Spread paper towel under the cooling rack to catch icing drippings.
While donuts are cooling, prepare the icing.
Heat up coconut milk and vanilla in the microwave for a few seconds (15-20 seconds). Place powder sugar in a bowl and coconut flakes in another bowl. Whisk in coconut milk mixture into powder sugar until all smooth.
Dip each donut into icing, covering top and sides. Dip them into coconut flakes and carefully place back on the wire rack.
Let them sit until completely cooled and icing is set.